You seem to suggest some kind of hidden variable theory for free will: https://en.wikipedia.org/wiki/Hidden-variable_theory. As far as I know they're not particularly popular among physicists, although we haven't (completely) ruled out such an explanation.
Newton and Einstein both seem to be on the side of hidden variables, so I'm not sure if it's unpopular among the elites.
I have a lot of trouble imagining any experiment which could completely rule out every other influencing factor. There are silly thought experiments such as what if the world has been objective for the last x00 years - prior to that and after, the laws we've observed during the period would bend; things will become inconsistent.
It's silly and I don't even believe it, but it does show that science is incapable of completely ruling out everything.
The truth could be endemic mystery. Endemic insanely and terrifyingly simple endless levels of understanding. In a way science is nothing unless that's the reality.
It's definitive that you have to give up locality (Bohmian mechanics), counterfactual definiteness (Copenhagen and others), or statistical independence (Superdeterminism). It's not definitive at all about local hidden variables.
Bell's theorem assumes statistical independence in its proof that local hidden variables can't reproduce QM. Superdeterminism violates statistical independence, therefore Bell's theorem does not rule out a superdeterministic local hidden variables theory, like this one:
